## Math 461. Probability Theory I

Instructor Syllabus

**Text: **Sheldon Ross, *A first Course in Probability*, *7th Edition*, Prentice Hall, 2006.

Chapter 1, Combinatorial Analysis, 4 hours

Chapter 2, Axioms of Probability (omit sections 2.6, 2.7), 5 hours

Chapter 3, Conditional Probability and Independence (omit section 3.5), 5 hours

Chapter 4, Random Variables (omit subsection 4.8.4), 6 hours

Chapter 5, Continuous Random Variables (omit subsections 5.5.1, 5.6.2, 5.6.4), 5 hours

Chapter 6, Jointly Distributed Random Variables (omit sections 6.6, 6.8), 5 hours

Chapter 7, Properties of Expectations (omit subsections 7.2.1, 7.2.2, 7.7.1, and section 7.9), 7 hours

Chapter 8, Limit Theorems (omit sections 8.4, 8.5, 8.6), 3 hours

Exams and leeway, 5 hours

Total: 45 hours

Note: Many students have difficulties with certain topics in calculus needed for this course, such as infinite series with positive terms (most calculations involve the geometric series and series derived from it), improper integrals and double integrals (change of variables formula, manipulating Gaussian integrals). Homework assignments and/or quizzes might help students to review this material.

If there is time left over, material from Chapter 9 or 10 can be covered. For chapter 10 students should have access to computers with appropriate software.

1/8/2008